name date - davis school district / overvie friends pooled the tickets they won from playing video...

Chapter 7 Skills Practice • 595

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Picture ThisPicture Algebra

Vocabulary 1. Write a definition for equation in your own words.

Problem SetDraw a picture to represent each situation. Label the unknown parts with variables and the known parts

with their values. Solve the problem and write an equation to represent the situation.

1. The ages of three siblings total 21 years. The middle child is one year older than the youngest, and

the eldest is three times as old as the youngest. How old is each child?

middle:21 totalyears

youngest: y

y

yeldest:

1

y y

3y 1 y 1 1 1 y 5 21 or 5y 1 1 5 21

The youngest child is 4 years old, the middle child is 5 years old, and the eldest child is

12 years old.

Lesson 7.1 Skills Practice

Name ________________________________________________________ Date _________________________

596 • Chapter 7 Skills Practice

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Lesson 7.1 Skills Practice page 2

2. Carly is making three cakes for the bake sale. The second cake requires 1 __ 2

cup more flour than

the first cake. The third cake requires twice the amount of flour as the first cake. The two-pound

bag of flour she bought has 8 1 __ 2 cups—exactly the amount she needs. How much flour is needed

for each cake?

3. Of the 1850 books in the library, there are four times as many books in the fiction section as are

in the nonfiction section. Also, there are 650 more books in the reference section than are in the

nonfiction section. How many books are in each section?


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Name ________________________________________________________ Date _________________________

4. Two friends pooled the tickets they won from playing video games to get a prize that requires

500 tickets. If one friend won 80 more tickets than the other friend, how many tickets did each

friend win?

5. There are 3900 workers in the three main buildings downtown. Twice as many people work in the

largest building as in the smallest of the three. There are 500 more workers in the second-largest

building than in the smallest building. How many workers are in each building?


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6. Lamar, Harris, and Tyler ran a 15-mile relay race as a team. Tyler ran 3 miles farther than Harris,

and Lamar ran twice as far as Harris. How many miles was each boy’s leg of the race?

7. The Petersons set aside $500 to donate to their three favorite charities: the children’s home, the

food bank, and the animal shelter. They gave twice as much to the food bank as to the animal

shelter. Their donation to the children’s home was $50 more than the donation to the food bank.

How much did each charity receive from the Petersons?


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Name ________________________________________________________ Date _________________________

8. There are 7000 middle-school students in the four middle schools in a city. There are three times

as many students at Hill Middle School than at Bell Middle School. There are twice as many

students at Ware Middle School than at Bell. Cane Middle School has 176 more students than

Ware. How many students are in each school?


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Maintaining a BalanceSolving Equations

VocabularyMatch the property of equality with its definition.

1. Addition Property of Equality

2. Subtraction Property of Equality

3. Multiplication Property of Equality

4. Division Property of Equality

a. if a 5 b, then a 1 c 5 b 1 c

b. if a 5 b, then ac 5 bc

c. if a 5 b, and c fi 0, then a __ c   5 b __ c 

d. if a 5 b, then a 2 c 5 b 2 c

Problem SetDetermine what will balance one rectangle. Explain your solution. Then rewrite each representation as

an equation.

1.

I subtracted 5 squares from each side which left 2 rectangles on one side and 4 squares on

the other side. Then I divided each side by 2 which left 1 rectangle on one side and 2 squares

on the other side.

1 rectangle 5 2 squares

2x 1 5 5 9


Name ________________________________________________________ Date _________________________


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2.

3.


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Name ________________________________________________________ Date _________________________

4.

5.


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6.

Solve each two-step equation. State the inverse operations, in the correct order of operations, you

used to isolate the variable. Check your solution.

7. 3w 2 17 5 4

Add first, and then divide. Check:

3w 2 17 5 4 3(7) 2 17 5 4

3w 2 17 1 17 5 4 1 17 21 2 17 5 4

3w 5 21 4 5 4

3w ___ 3 5 21 ___

3

w 5 7


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Name ________________________________________________________ Date _________________________

8. 25 1 8x 5 65

9. 94 5 y __

4 2 18


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10. g

 __ 9

1 47 5 64

11. 72 5 5h 1 22


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Name ________________________________________________________ Date _________________________

12. c ___ 20

2 41 5 59

13. 138 5 7h 1 5


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14. 16 5 8 1 p

 __ 2

Solve each riddle using equations.

15. What is a number that when you multiply it by 3 and subtract 12 from the product, you get 12?

3x 2 12 5 12

3x 5 24

      x 5 8

The number is 8.


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Name ________________________________________________________ Date _________________________

16. What is a number that when you multiply it by 7 and add 25 to the product, you get 46?




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Planning a Graduation PartySolving Two-Step Equations

Vocabulary 1. Give an example of a two-step equation and describe the steps you would use to solve it.

Problem SetWrite a sentence to describe how to apply inverse operations to solve each equation. Then, solve the

equation and verify your solution.

1. 4x 1 12 5 24

First subtract 12 from each side, then divide each side by 4.

4x 1 12 5 24

4x 1 12 2 12 5 24 2 12

4x ___ 4

5 12 ___ 4

            x 5 3

Verify the solution by substituting 3 for x in the equation.

4(3) 1 12 0 24

24 5 24


Name ________________________________________________________ Date _________________________


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2. 25 2 8x 5 215

3. 13 2 x __ 7 5 6


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Name ________________________________________________________ Date _________________________

4. 25x 2 12 5 18

5. x __ 9

1 29 5 41


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6. 42 5 27x 1 35

7. 28 5 2x 2 14


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Name ________________________________________________________ Date _________________________

8. 21 5 36 2 x ___ 30

9. 219 5 35 1 9x


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10. 11x 1 13 5 29


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Name ________________________________________________________ Date _________________________

Write an equation to represent each situation. Define your variables, solve the equation, and verify

your solution.

11. Ms. Moderelli charges her piano students $40 per lesson plus a semester recital fee of $55.

How many lessons did Jerry take if he paid a total of $695 for lessons this semester?

40p 1 55 5 695

Let p represent the number of lessons taken during the semester.

40p 1 55 5 695

40p 1 55 2 55 5 695 2 55

40p

 ____ 40

5 640 ____ 40

p 5 16

Jerry took 16 lessons.

Verify the solution by substituting 16 for p in the equation.

40(16) 1 55 0 695

695 5 695


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12. The Sunshine Nursery offers a spring flower deal. If a customer purchases at least one flat of

6 annuals, they will receive 3 free perennials. How many flats of annuals must you buy to get a

total of 21 plants?


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Name ________________________________________________________ Date _________________________

13. The student council ordered 1000 pencils embossed with the school name to give to honor roll

students. If they give each honor roll student two pencils and they have 840 pencils left after the

first quarter, how many students are on the honor roll in the first quarter?


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14. Craig and four of his friends had a car wash to earn some extra money. They split the profits and

Craig got an extra $18 to repay his parents for the car wash supplies. If Craig got $32, how much

total money did they split among themselves?


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Name ________________________________________________________ Date _________________________

15. Javier has a collection of 125 comic books. He gives each of his 3 friends the same number of

comic books and keeps his favorite 38 comic books for himself. How many comic books did he

give to each of his friends?


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16. Tyler is planning a party at a restaurant. There is a flat fee of $250 to reserve the restaurant for the

evening and a charge of $20 per person for food and drink. If Tyler has $500 to spend, what is the

maximum number of people that can attend the party?


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Solving in Big-Time StyleUsing Two-Step Equations

Problem SetSolve each equation using the Distributive Property.


Name ________________________________________________________ Date _________________________

1. 6(x 1 1) 1 5 5 35

6(x 1 1) 1 5 5 35

6x 1 6 1 5 5 35

6x 1 11 5 35

6x 1 11 2 11 5 35 2 11

6x ___ 6

5 24 ___ 6

                    x 5 4

2. 214 5 22(5 2 x) 1 16

3. 3(2x 1 7) 2 3x 5 18 4. 0.7(x 2 2) 5 0.3


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5. 1.95(6.2 2 3x) 2 4.81 5 218.46 6. 28 5 14 1 7(x 2 6)

7. 78 5 29x 2 3(256 1 12x) 8. 0.20x 2 0.08(x 2 10) 5 24.80


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Name ________________________________________________________ Date _________________________

9. 7(4x 1 9) 2 13 5 287 10. 0.25(3 2 x) 5 0.375


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Write an equation to represent each situation. Define your variables and solve the equation.

11. At the Namaste Yoga Studio, the first two yoga classes you take are free with your registration fee

of $15. Each class after that is $45. How many classes can you take for $1185?

1185 5 15 1 45(x 2 2)

Let y represent the total amount paid and x represent the number of classes taken.

1185 5 15 1 45x 2 90

1185 5 45x 2 75

1185 1 75 5 45x 2 75 1 75

1260 _____ 45

5 45x ____ 45

28 5 x

You can take 28 yoga classes for $1185 dollars.

12. Clara has a coupon for $10 off at her favorite clothing store. The coupon is applied before any

discounts are taken. The store is having a sale, and offering 15% off everything. If Clara has $50

to spend, how much can her purchases total before applying the discount and her coupon?

Round to the nearest cent.


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Name ________________________________________________________ Date _________________________

13. Nico bought groceries for the week. He used his debit card to pay for the groceries, including sales

tax, and added $25 cash back. If the groceries totaled $138.24 before tax, and the total debited

from his account was $173.61, what percentage was the sales tax? Round to the nearest tenth

of a percent.


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14. A party store uses 20% of a tank of helium a day and fills 80 balloons. Each balloon takes

0.5 cubic feet of helium to fill. How many cubic feet of helium are in a full tank?

15. Susana bought a laptop for $500. It was marked $50 off because it was out of the box and slightly

scratched. She also got a 25% student discount, which was taken off of the original price. What

was the original price of the laptop?


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Name ________________________________________________________ Date _________________________

16. A dog kennel charges $40 to board a dog for one night and $35 per night each night after that.

Henry paid a total of $215 for dog boarding. For how many nights did Henry board his dog?


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Name ________________________________________________________ Date _________________________

We’re Shipping Out!Solving and Graphing Inequalities in One Variable

VocabularyUse the words “graph,” “solve,” or “reverse” to best complete each sentence.

1. You an inequality when you determine the values of the variable that make the

inequality true.

2. You the inequality symbol when you multiply or divide each side of an

inequality by a negative value.

3. You an inequality on a number line with an open or closed circle and a ray.

Problem SetWrite an inequality for each situation.

1. Tyler needs to buy a book for school that costs $13. He also wants to get a book for each of his

two sisters and he wants to be sure he spends the same amount on each of their books. He only

has $27 to spend. Let b represent the amount he can spend on each additional book.

13 1 2b # 27

2. Ming rents a cart for her bike to carry tools and wood to school for her science project. Her

toolbox weighs 20 pounds and the cart can carry a maximum of 50 pounds. Each wood board

weighs 3 pounds. Let w represent the number of wood boards she can carry.

3. There must be less than 36 people on one bus. There are already 17 people on the bus. Let p

represent the additional number of people that can ride the bus.

4. A family of three has a coupon for $5 off their total bill when everyone orders the same meal.

The family has $40 to spend on dinner. Let m represent the cost of the meal they can order.


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5. Vijay wants to keep the cost per person of his party under $15. The Party Place charges a flat fee

of $250 for an all-inclusive party. Let g represent the number of guests, including himself, he can

invite.

6. The temperature of the liquid starts at 72°F and drops 2 degrees per second. The liquid is not to

go below 40°F. Let s represent the number of seconds.

A list of possible solutions for each inequality is shown. Choose the solutions that make the inequality

true. Then, list three additional solutions to the inequality.

7. x . 2

22, 21, 0, 1, 2, 3, 4, 5, 6, 7

The numbers 3, 4, 5, 6, and 7 make the inequality true.

Answers will vary. Three additional solutions for the inequality are 8, 9, and 10.

8. 5x , 30

22, 21, 0, 1, 2, 3, 4, 5, 6, 7

9. 2x 1 7 $ 5

22, 21, 0, 1, 2, 3, 4, 5, 6, 7

10. 8 # 24x

22, 21, 0, 1, 2, 3, 4, 5, 6, 7


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Name ________________________________________________________ Date _________________________

11. 3x 2 1 # 14

22, 21, 0, 1, 2, 3, 4, 5, 6, 7

12. 4 , x __ 3 1 2

22, 21, 0, 1, 2, 3, 4, 5, 6, 7

Solve each inequality and then graph the solution.

13. 8x . 56

8x . 56

8x ___ 8

. 56 ___ 8

x . 7

0 1 2 3 4 5 6 7 8 9 10 11 12

14. 144 $ 212x


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Name ________________________________________________________ Date _________________________

17. 21 2 9x $ 26

18. 78 . 4x 1 6

name date - davis school district / overvie friends pooled the tickets they won from playing video...

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